What are some new deep learning models for learning latent representation of data?
Here's a link to my answer on CV Stack Exchange, where I have mentioned about latent spaces and some deep learning models that learn these representations: https://stats.stackexchange.com/questions/442352/what-is-a-latent-space/442360#442360

In short, deep learning models for Domain Adaptation, Computer Vision, Natural Language Processing, Recommendation Systems, Music/Speech/Audio processing, Adversarial models, etc., all learn some form of latent representation of data.

In fact, any place we're learning a function to map input and output spaces of a dataset, the model essentially learns a latent representation of data irrespective of whether the model is based on deep neural networks or a stochastic method or any other.